Self-Normalized Processes : Limit Theory and Statistical Applications

This volume covers recent developments in self-normalized processes, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales.

Independent Random Variables.- Classical Limit Theorems, Inequalities and Other Tools.- Self-Normalized Large Deviations.- Weak Convergence of Self-Normalized Sums.- Stein''s Method and Self-Normalized Berry-Esseen Inequality.- Self-Normalized Moderate Deviations and Laws of the Iterated Logarithm.- Cramér-Type Moderate Deviations for Self-Normalized Sums.- Self-Normalized Empirical Processes and U-Statistics.- Martingales and Dependent Random Vectors.- Martingale Inequalities and Related Tools.- A General Framework for Self-Normalization.- Pseudo-Maximization via Method of Mixtures.- Moment and Exponential Inequalities for Self-Normalized Processes.- Laws of the Iterated Logarithm for Self-Normalized Processes.- Multivariate Self-Normalized Processes with Matrix Normalization.- Statistical Applications.- The t-Statistic and Studentized Statistics.- Self-Normalization for Approximate Pivots in Bootstrapping.- Pseudo-Maximization in Likelihood and Bayesian Inference.- Sequential Analysis and Boundary Crossing Probabilities for Self-Normalized Statistics.